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Global Smoothness Preservation by General Operators

In: Approximation Theory

Author

Listed:
  • George A. Anastassiou

    (University of Memphis, Department of Mathematical Sciences)

  • Sorin G. Gal

    (University of Oradea, Department of Mathematics)

Abstract

In this chapter we search the conditions under which global smoothness of a function f (as measured by its modulus of continuity) is preserved by the elements of general approximating sequences (L n f). As one consequence we obtain statements concerning the invariance of Lipschitz classes under operators of several types. An important tool in our approach is the least concave majorant of a modulus of continuity. Here we follow the basic study done by the first author, Cottin and Gonska [22].

Suggested Citation

  • George A. Anastassiou & Sorin G. Gal, 2000. "Global Smoothness Preservation by General Operators," Springer Books, in: Approximation Theory, chapter 7, pages 231-249, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1360-4_7
    DOI: 10.1007/978-1-4612-1360-4_7
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